It is advantageous to use an air-cooled internal combustion engine for a small outboard marine drive in view of reducing weight. Such an engine requires fresh cooling air to be continuously supplied for preventing the overheating of the engine. For aesthetic considerations and convenience of handling, it is desirable to cover the engine. Thus, conflicting requirements are imposed on small outboard marine engines. According to the invention disclosed in Japanese UM publication (kokoku) No. 2-23782, a cover is placed over the cylinder head of an outboard marine engine while the crankcase thereof is exposed. However, the aesthetic considerations are extremely important, and it is desired to minimize the exposure of the internal combustion engine.